Concyclic Points.

Suppose there exists a triangle $\triangle{ABC}$ where $P$ and $Q$ are points on segments $\overline{AB}$ and $\overline{AC}$ respectively, such that:

(1) $\overline{AP} = \overline{AQ}$ .

Let $S$ and $R$ be distinct points on segment $\overline{BC}$ such that:

(2) $S$ lies between points $B$ and $R$

(3) $\angle{BPS} = \angle{PRS}$ , and $\angle{CQR} = \angle{QSR}$ .

Prove that points $P,Q,R,S$ are concyclic points.

#Geometry #Angles #Concyclic #Proofs #Triangles

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$